As news of the successful conclusion of preliminary nuclear negotiations between Iran and six nations spread through the Iranian capital Tehran early Sunday morning, reactions were overwhelmingly positive. Congratulatory notes flooded Twitter, sent and received by tech-savvy Iranians circumventing Internet firewalls put up by the government. “CONGRATULATIONS Iran back in the picture will create a diplomatic and economic tsunami,” read one popular tweet making the rounds in English. Even Iranians abroad broadcast their felicitations. “A dark decade just ended tonight in Geneva. A new era just started for #Iran,” tweeted Iranian-American TV host Negar Mortazavi.

It wasn’t just the prospect of reduced sanctions that had Iranians celebrating. As a clearly fatigued Mohammad Javad Zarif, Iran’s Foreign Minister and principal nuclear negotiator, posted on Facebook at 4 a.m. Geneva time, Iran felt that its right to enrich nuclear material had been preserved. “Enrichment was recognized,” he wrote, although the exact wording of the deal does not explicitly offer formal recognition. It was a diplomatic take on a key point of pride for the Iranians that had threatened to scuttle the talks entirely. A few hours later, Iranian President Hassan Rouhani broadcast a statement on national television that the deal “recognized Iran’s nuclear rights,” and that talks on a comprehensive, long-lasting deal “will start immediately.”

“It was clearly a tough round of talks,” Amir Mohebian, a Tehran-based political analyst with centrist leanings, tells TIME. “But each side thinks it emerged the winner.” Iranians, he said, were very happy, not least because many feared that failed talks might end in increased hostilities or even war. In addition, sanctions have been a huge burden on the country’s economy. Even though the temporary deal, which calls for a limit on enrichment activities in exchange for freeing up some $7 billion of Iranian funds frozen in foreign bank accounts, only mitigates a fraction of Iran’s annual economic losses the sanctions regime has inflicted, Iranians are optimistic. “Definitely people understand it was hard, but people think the results of negotiations were good for Iran, because now we have the possibility to rebuild our economic interests,” says Mohebian.

The deal clears the way for more comprehensive negotiations about the shape and future of Iran’s whole nuclear program. Those talks, whose goal would be to ensure that Iran’s nuclear program remains purely civilian in nature, are due to take place over the next six months. The outcome of those discussions is by no means guaranteed, and there are sure to be many stumbling blocks ahead. But to Mohebian, the first step was the hardest.

“For 25 years hostilities between Iran and the United States was an uncrossable chasm, but with these negotiations we have built a bridge,” he says. “We have broken the taboo of meeting face to face.”

In Iran, hard-liners may not be happy, but they are likely to remain subdued. No deal could have happened without the approval of Iran’s powerful Supreme Leader Ali Khamenei, who had earlier declared the negotiators to be “children of the revolution.”

U.S. Secretary of State John Kerry’s team may not fare so well in the U.S., says Mohebian. The vocal anti-Iran rhetoric coming from Congress has not gone unnoticed in Tehran, where some Iranians are more concerned about hard-liners in the U.S. potentially scuttling a future agreement than they are about conservatives at home. “We think the situation for Obama and Kerry is actually more difficult because Congress will be against this agreement, because of the Arab and Israeli lobbies,” says Mohebian. “I don’t think that the people in Congress and in Israel and the Arab countries who are criticizing the negotiations understand that what Obama and Kerry have done is useful for peaceful relations between Iran and the United States. Don’t they understand that it is better than war?”

Aryn Baker is the Middle East Bureau Chief for TIME, covering politics, society, culture, religion, the arts and the military in the greater Middle East, including Pakistan and Afghanistan. She currently resides in Beirut, Lebanon.